Analyticity of gluon and Faddeev--Popov ghost propagators and their form
factors on the complex momentum-squared plane is exploited to continue
analytically the ultraviolet asymptotic form calculable by perturbation theory
into the infrared non-perturbative solution. We require the non-perturbative
multiplicative renormalizability to write down the renormalization group
equation. These requirements enable one to settle the value of the exponent
characterizing the infrared asymptotic solution with power behavior which was
originally predicted by Gribov and has recently been found as approximate
solutions of the coupled truncated Schwinger--Dyson equations. For this
purpose, we have obtained all the possible superconvergence relations for the
propagators and form factors in both the generalized Lorentz gauge and the
modified Maximal Abelian gauge. We show that the transverse gluon propagators
are suppressed in the infrared region to be of the massive type irrespective of
the gauge parameter, in agreement with the recent result of numerical
simulations on a lattice. However, this method alone is not sufficient to
specify some of the ghost propagators which play the crucial role in color
confinement. Combining the above result with the renormalization group equation
again, we find an infrared enhanced asymptotic solution for the ghost
propagator. The coupled solutions fulfill the color confinement criterion due
to Kugo and Ojima and also Nishijima, at least, in the Lorentz--Landau gauge.
We also point out that the solution in compatible with color confinement leads
to the existence of the infrared fixed point in pure Yang--Mills theory without
dynamical quarks. Finally, the Maximal Abelian gauge is also examined in
connection with quark confinement.Comment: 60 pages, 11 figure